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A parafermionic hypergeometric function and supersymmetric 6j-symbols
Elena Apresyan, Gor Sarkissian, Vyacheslav P. Spiridonov
We study properties of a parafermionic generalization of the hyperbolic hypergeometric function appearing as the most important part in the fusion matrix for Liouville field theory…
Superconformal indices, Seiberg dualities and special functions
Vyacheslav P. Spiridonov
This is a brief account of relations between the theory of special functions, on the one side, and superconformal indices and Seiberg dualities of four-dimensional …
General modular quantum dilogarithm and beta integrals
Gor Sarkissian, Vyacheslav P. Spiridonov
We consider a univariate beta integral composed from general modular quantum dilogarithm functions and prove its exact evaluation formula. It represents the partition function of a…
From rarefied elliptic beta integral to parafermionic star-triangle relation
Gor Sarkissian, Vyacheslav P. Spiridonov
We consider the rarefied elliptic beta integral in various limiting forms. In particular, we obtain an integral identity for parafermionic hyperbolic gamma functions which describe…
4d quiver gauge theories and the Bailey lemma
Frederic Brünner, Vyacheslav P. Spiridonov
We study the integral Bailey lemma associated with the -root system and identities for elliptic hypergeometric integrals generated thereby. Interpreting integrals as…
Supersymmetric Casimir Energy and Transformations
Frederic Brünner, Diego Regalado, Vyacheslav P. Spiridonov
We provide a recipe to extract the supersymmetric Casimir energy of theories defined on primary Hopf surfaces directly from the superconformal index. It involves an $\mathrm{SL(3,\…